A previously unexplored method, combining logical and mathematical elements, is shown to yield substantial numerical improvements in the area of Diophantine approximations. Kreisel illustrated the method abstractly by noting that effective bounds on the number of elements are ensured if Herbrand terms from ineffective proofs ofΣ2-finiteness theorems satisfy certain simple growth conditions. Here several efficient growth conditions for the same purpose are presented that are actually satisfied in practice, in particular, by the proofs of Roth's theorem due to (...) Roth himself and to Esnault and Viehweg. The analysis of the former yields an exponential bound of order exp in place of exp given by Davenport and Roth in 1955, whereαis algebraic of degreed≥ 2 and ∣α−pq−1∣ shrink)

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

We define a new type of “shatter function” for set systems that satisfies a Sauer–Shelah type dichotomy, but whose polynomial-growth case is governed by Shelah’s two-rank instead of VC dimension. We identify the least exponent bounding the rate of growth of the shatter function, the quantity analogous to VC density, with Shelah’s $\omega $ -rank.

This paper develops the foundations of the descriptive set theory of countable Borel equivalence relations on Polish spaces with particular emphasis on the study of hyperfinite, amenable, treeable and universal equivalence relations.

A previously unexplored method, combining logical and mathematical elements, is shown to yield substantial numerical improvements in the area of Diophantine approximations. Kreisel illustrated the method abstractly by noting that effective bounds on the number of elements are ensured if Herbrand terms from ineffective proofs of Σ 2 -finiteness theorems satisfy certain simple growth conditions. Here several efficient growth conditions for the same purpose are presented that are actually satisfied in practice, in particular, by the proofs of Roth's (...) theorem due to Roth himself and to Esnault and Viehweg. The analysis of the former yields an exponential bound of order exp(70ε -2 d 2 ) in place of exp(285ε -2 d 2 ) given by Davenport and Roth in 1955, where α is (real) algebraic of degree d ≥ 2 and $|\alpha - pq^{-1}| . (Thus the new bound is less than the fourth root of the old one.) The new bounds extracted from the other proof are polynomial of low degree (in ε -1 and log d). Corollaries: Apart from a new bound for the number of solutions of the corresponding Diophantine equations and inequalities (among them Thue's inequality), $\log \log q_\nu , where q ν are the denominators of the convergents to the continued fraction of α. (shrink)

This paper classifies a family of grammar formalisms that extendcontext-free grammar by talking about tuples of terminal strings, ratherthan independently combining single terminal words into larger singlephrases. These include a number of well-known formalisms, such as headgrammar and linear context-free rewriting systems, but also a new formalism,(simple) literal movement grammar, which strictly extends the previouslyknown formalisms, while preserving polynomial time recognizability.The descriptive capacity of simple literal movement grammars isillustrated both formally through a weak generative capacity argument and ina more (...) practical sense by the description of conjunctive cross-serialrelative clauses in Dutch. After sketching a complexity result and drawing anumber of conclusions from the illustrations, it is then suggested that thenotion of mild context-sensitivity currently in use, that depends on therather loosely defined concept of constant growth, needs a modification toapply sensibly to the illustrated facts; an attempt at such a revision isproposed. (shrink)

In computer science, an algorithm is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing and automated reasoning tasks. As an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, (...) eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input. This book introduces a set of concepts in solving problems computationally such as Growth of Functions; Backtracking; Divide and Conquer; Greedy Algorithms; Dynamic Programming; Elementary Graph Algorithms; Minimal Spanning Tree; Single-Source Shortest Paths; All Pairs Shortest Paths; Flow Networks; Polynomial Multiplication, to ways of solving NP-Complete Problems, supported with comprehensive, and detailed problems and solutions, making it an ideal resource to those studying computer science, computer engineering and information technology. (shrink)

We study the extension of public announcement logic PAL by public assignments, which we call PALA. Just as in the case of PAL, the standard procedure for deciding PALA validity, i.e. the use of so-called reduction axioms to translate PALA formulae into formulae in epistemic logic EL, may lead to exponential growth. In this paper, we show that such a price is not mandatory, for we provide a polynomial translation of PALA into EL. This is based on abbreviations (...) of subformulae by new propositional letters. Such optimal translation also enables us to show the computational complexity of the problem of deciding PALA validity, which turns out to be coNP-complete in the single-agent case and PSPACE-complete in the multiagent case. (shrink)

Kolmogorov complexity was originally defined for finitely-representable objects. Later, the definition was extended to real numbers based on the asymptotic behaviour of the sequence of the Kolmogorov complexities of the finitely-representable objects—such as rational numbers—used to approximate them.This idea will be taken further here by extending the definition to continuous functions over real numbers, based on the fact that every continuous real function can be represented as the limit of a sequence of finitely-representable enclosures, such as polynomials with rational coefficients.Based (...) on this definition, we will prove that for any growth rate imaginable, there are real functions whose Kolmogorov complexities have higher growth rates. In fact, using the concept of prevalence, we will prove that ‘almost every’ continuous real function has such a high-growth Kolmogorov complexity. An asymptotic bound on the Kolmogorov complexities of total single-valued computable real functions will be presented as well. (shrink)

This paper defines natural hierarchies of function and relation classes □i,kc and Δi,kc, constructed from parallel complexity classes in a manner analogous to the polynomial-time hierarchy. It is easily shown that □i−1,kp □c,kc □i,kp and similarly for the Δ classes. The class □i,3c coincides with the single-valued functions in Buss et al.'s class , and analogously for other growth rates. Furthermore, the class □i,kc comprises exactly the functions Σi,kb-definable in Ski−1, and if Tki−1 is Σi,kb-conservative over Ski−1, then (...) □i,kp is completely parallelizable. All functions in □i,kc are Σi,kb-definable in Rki; this suffices to show that if the known Σi,kb conservativity between R3i and S3i−1 extends to R2i and S2i−1, then NC = NC1 relative to an oracle in PH. We prove a KPT-style witnessing theorem for Ski using constantly many rounds of □i,kc interactive computation, and thus show that if Ski ≡ Rki+1 then the bounded arithmetic hierarchy collapses, provably in Ski. (shrink)

A twenty‐person working group convened to discuss the ethical and policy considerations of the controversial intervention called “growth attenuation,” and if possible to develop practical guidance for health professionals. A consensus proved elusive, but most of the members did reach a compromise.

This volume examines some of the arguments that have been put forward over the years to explain the way in which understanding is acquired. The author looks firstly at the empricist thesis of genesis without structure, and secondly at the opposing theory, represented by Chomsky of structure without genesis. His greatest sympathy is with the theory of Piaget, who represents structure with genesis. He considers that Piaget's account is flawed, however, by its biological model and by its failure to deal (...) adequately with the problem of objectivity. The second part of the book contains chapters on language, the differences between early and later learning, and on teaching. The book provides a general understanding of the principles that make it possible, and the differences between the ways in which they work at different stages. (shrink)

Three hundred and seventy-six middle school students in Wenchuan County were assessed three and one-half years after the Wenchuan earthquake to examine the effects of rumination on posttraumatic stress disorder (PTSD) and posttraumatic growth (PTG). The results revealed that recent intrusive ruminations partly mediated the relationship between intrusive rumination soon after the earthquake with PTSD but not with PTG. Recent deliberate rumination partly mediated the relationship between intrusive rumination soon after the earthquake and PTG but not PTSD. Moreover, recent (...) deliberate rumination also partly mediated the relationship between recent intrusive rumination with PTG but not with PTSD. Overall, intrusive rumination soon after the earthquake had an effect on PTSD but not on PTG through recent intrusive rumination and affected PTG but not PTSD through deliberate recent rumination. Furthermore, intrusive rumination soon after the earthquake affected PTG but not PTSD by recent deliberate rumination following recent intrusive rumination. More importantly, the present study also found that PTSD exhibited no relation to PTG. These results suggest that PTSD and PTG are influenced by different mechanisms, which further indicates that PTSD and PTG represent two separate dimensions of experience after adversity. (shrink)

Parameters of a Bertalanffy type of temperature dependent growth model are fitted using data from a population of stone loach ( Barbatula barbatula ). Over two periods respectively in 1990 and 2010 length data of this population has been collected at a lowland stream in the central part of the Netherlands. The estimation of the maximum length of a fully grown individual is given special attention because it is in fact found as the result of an extrapolation over a (...) large interval of the entire lifetime. It is concluded that this parameter should not at forehand be set at one fixed value for the population at that location due to varying conditions over the years. (shrink)

This paper proposes two interrelated arguments: first, it is argued that agro-commodity traders are uniquely placed at the crossroads of agricultural trade to benefit from agricultural commodity speculation; and second, that the networks constituting their operations are central to their hedging activities. The case of Cargill—the largest privately owned company in the United States and one of the largest agricultural traders in the world—is used to support this argument by unpacking its operations, structure, and hedging strategies. In order to connect (...) the operations of Cargill to its speculating strategies, this paper first traces how agriculture and finance have become increasingly intertwined leading to heightened agricultural commodity speculation. Second, Cargill will be positioned within this process by analyzing how it has financialized its own strategies and its Corporate Platform. Third, Black River Asset Management, Cargill’s private equity arm, will be analyzed to show how it uses the information moving through Cargill’s Platform to engage in hedging and/or speculation. (shrink)

For decades futurists, academics and business experts have argued that automation, robots and other new technology would eliminate millions of jobs. Yet the workforce in the US has continued to grow, even if more slowly, to new heights. Work has changed, but the predicted ‘end of work’ failed to materialise even as technology has advanced, albeit unevenly. This article will argue that the answer to this apparent riddle is not to be found in analysing the technology itself, but in Marxist (...) political economy. The progress of robots and related technology will be examined, but the argument is that the limits on technical progress in the actual production of goods and services lie in the turbulence of capitalism since the 1970s with its uneven profit rates. (shrink)

As previous pandemics, the coronavirus disease 2019 (COVID-19) has direct and indirect effects on mental health and well-being. The purpose of the current study was to examine whether meaning in life mediated the association between coronavirus suffering and satisfaction with life and whether stress-related growth moderated the mediating effect of meaning in life on the association between these variables. Stress-Related Growth Measure (SGM) was also conducted for the purpose of this study. The participants were 402 (66% women) young (...) adults who completed the Suffering Measure During COVID-19, Meaningful Living Measure, Satisfaction With Life Scale, and SGM. The results indicated that the SGM has adequate psychometric properties with unidimensional structure of stress-related growth in the face of adversity. Moderated mediation analysis revealed that coronavirus suffering directly influenced satisfaction with life as well as indirectly by its effect on meaning in life. Additionally, stress-related growth was found as a moderator in the relationship between coronavirus suffering–meaning in life and coronavirus suffering–satisfaction with life. These results suggest that meaning in life mitigates the effect of coronavirus suffering on satisfaction with life, and this mediating effect is moderated by stress-related growth in young adults. While meaning in life helps explain the relationship between coronavirus suffering and satisfaction with life, the stress-related growth functions as a protective factor against the adverse effect of coronavirus experiences. (shrink)

Purpose:On the background of innovation-driven growth strategy of the Chinese government, this study aims to explore the impact of the knowledge base on innovation-driven growth of a firm, which is moderated by organizational character.Design/methodology/approach:Based on the data of 965 Chinese listed companies, some hypotheses were tested using the method of hierarchical regression analysis.Findings:Organizational growth relies on both technological and business model innovations and their interactive effect. Knowledge base, both breadth and depth, makes a positive impact on the (...) innovation-driven growth of an enterprise. In the impacting mechanism, an explicit organizational character not only has direct positive effects on business model innovation, it also strengthens the effect of knowledge breadth on business model innovation. On the contrary, an implicit organizational character is not significantly related to innovation.Research limitations/implications:In order to achieve growth, enterprises are suggested to adopt such dual innovation strategy, led by technological innovation and supplemented with business model innovation, which is supported by the integrated management of intangible resources, deep and broad knowledge, and explicit organizational character.Originality/value:A new theoretical framework of organizational innovation-driven growth was proposed. The realization paths of innovation-driven growth were explored. The idea of collaborative governance between the knowledge base and organizational character was raised. (shrink)

This handbook by Allan Harkness will give you a variety of practical and creative ideas for making time with God a significant part of your life. You don't need any special qualifications. Are you ready to grow?

The paper gives an introduction to the problem whether there is a logic ℒ that captures PTIME in the sense that, via some natural encoding, the classes of finite structures axiomatizable in ℒ correspond to the languages in PTIME. It discusses several notions of capturing, thereby giving a picture of the general theory. The question for the most important version is still open. The paper surveys positive answers for certain classes of graphs that are based on the method of canonization.

Given a prime p, we exhibit a Horn sentence H p which expresses "the cardinality is not p" and has size O(p 5 log p).

We give a term rewriting characterization of the polyspace functions. Our work follows investigations on term rewriting characterizations of some classes of (sub-) recursive functions as initiated by Cichon and Weiermann [4] and continued by Beckmann and Weiermann [1].The main novelty of this paper is a technique for reformulating recursion schemes. The aim of this technique is to provide rewriting rules which give rise to rewriting chains whose terms are suitably bounded. This bounding is crucial when dealing with computational classes (...) with space constraints. (shrink)